Find the Unit Tangent Vector of the Given Curve A) $\mathrm { T } = \frac { 2 } { 225 } \mathrm { i } + \frac { 2 } { 45 } \mathrm { j } + \frac { 11 } { 225 } \mathbf { k }$

question 133

Multiple Choice

Find the unit tangent vector of the given curve.
- $$\mathbf { r } ( \mathrm { t } ) = \left( 5 + 2 \mathrm { t } ^ { 8 } \right) \mathbf { i } + \left( 3 + 10 \mathrm { t } ^ { 8 } \right) \mathbf { j } + \left( 5 + 11 t ^ { 8 } \right) \mathbf { k }$$

• A) \(\mathrm { T } = \frac { 2 } { 225 } \mathrm { i } + \frac { 2 } { 45 } \mathrm { j } + \frac { 11 } { 225 } \mathbf { k }\)
• B) \(\mathrm { T } = \frac { 2 } { 15 } \mathrm { i } + \frac { 2 } { 3 } \mathrm { j } + \frac { 11 } { 15 } \mathbf { k }\)
• C) \(\mathbf { T } = \frac { 16 } { 15 } \mathbf { i } + \frac { 16 } { 3 } \mathbf { j } + \frac { 88 } { 15 } \mathbf { k }\)
• D) \(\mathbf { T } = 2 \mathbf { i } + 10 \mathbf { j } + 11 \mathbf { k }\)

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Tropic Interactions

Ecological interactions that cause organisms to move or grow toward or away from stimuli, including phototropism, hydrotropism, and others.

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